Roberto M. Cesar

Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification

We present a method for automated segmentation of the vasculature in retinal images. The method produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixels feature vector. Feature vectors are composed of the pixels intensity and two-dimensional Gabor wavelet transform responses taken at multiple scales. The Gabor wavelet is capable of tuning to specific frequencies, thus allowing noise filtering and vessel enhancement in a single step. We use a Bayesian classifier with class-conditional probability density functions (likelihoods) described as Gaussian mixtures, yielding a fast classification, while being able to model complex decision surfaces. The probability distributions are estimated based on a training set of labeled pixels obtained from manual segmentations. The methods performance is evaluated on publicly available DRIVE (Staal et al.,2004) and STARE (Hoover et al.,2000) databases of manually labeled images. On the DRIVE database, it achieves an area under the receiver operating characteristic curve of 0.9614, being slightly superior than that presented by state-of-the-art approaches. We are making our implementation available as open source MATLAB scripts for researchers interested in implementation details, evaluation, or development of methods

Inference from Clustering with Application to Gene-Expression Microarrays

There are many algorithms to cluster sample data points based on nearness or a similarity measure. Often the implication is that points in different clusters come from different underlying classes, whereas those in the same cluster come from the same class. Stochastically, the underlying classes represent different random processes. The inference is that clusters represent a partition of the sample points according to which process they belong. This paper discusses a model-based clustering toolbox that evaluates cluster accuracy. Each random process is modeled as its mean plus independent noise, sample points are generated, the points are clustered, and the clustering error is the number of points clustered incorrectly according to the generating random processes. Various clustering algorithms are evaluated based on process variance and the key issue of the rate at which algorithmic performance improves with increasing numbers of experimental replications. The model means can be selected by hand to test the separability of expected types of biological expression patterns. Alternatively, the model can be seeded by real data to test the expected precision of that output or the extent of improvement in precision that replication could provide. In the latter case, a clustering algorithm is used to form clusters, and the model is seeded with the means and variances of these clusters. Other algorithms are then tested relative to the seeding algorithm. Results are averaged over various seeds. Output includes error tables and graphs, confusion matrices, principal-component plots, and validation measures. Five algorithms are studied in detail: K-means, fuzzy C-means, self-organizing maps, hierarchical Euclidean-distance-based and correlation-based clustering. The toolbox is applied to gene-expression clustering based on cDNA microarrays using real data. Expression profile graphics are generated and error analysis is displayed within the context of these profile graphics. A large amount of generated output is available over the web.

Inexact graph matching for model-based recognition: Evaluation and comparison of optimization algorithms

A method for segmentation and recognition of image structures based on graph homomorphisms is presented in this paper. It is a model-based recognition method where the input image is over-segmented and the obtained regions are represented by an attributed relational graph (ARG). This graph is then matched against a model graph thus accomplishing the model-based recognition task. This type of problem calls for inexact graph matching through a homomorphism between the graphs since no bijective correspondence can be expected, because of the over-segmentation of the image with respect to the model. The search for the best homomorphism is carried out by optimizing an objective function based on similarities between object and relational attributes defined on the graphs. The following optimization procedures are compared and discussed: deterministic tree search, for which new algorithms are detailed, genetic algorithms and estimation of distribution algorithms. In order to assess the performance of these algorithms using real data, experimental results on supervised classification of facial features using face images from public databases are presented.

Shape characterization with the wavelet transform

We present a new approach to the problem of two-dimensional multiscale shape representation and analysis, based on the one-dimensional continuous wavelet transform (CWT). The shape is represented by the complex signal that describes its boundary, and the CWT is applied to this signal, leading to the so-called W-representation. Wavelet theory provides the W-representation with several properties that are generally required from shape representation frameworks. In addition, we introduce algorithms for extracting meaningful information about the shape from its W-representation, for instance, detection of dominant points and shape partitioning, natural scales analysis, and fractal-based analysis. The algorithms that accomplish these tasks are tested on shapes obtained from synthetic and real images. Thus the W-representation yields a unified approach to a number of important problems of shape characterization for purposes of machine vision

Automated segmentation of retinal blood vessels and identification of proliferative diabetic retinopathy

Proliferative diabetic retinopathy can lead to blindness. However, early recognition allows appropriate, timely intervention. Fluorescein-labeled retinal blood vessels of 27 digital images were automatically segmented using the Gabor wavelet transform and classified using traditional features such as area, perimeter, and an additional five morphological features based on the derivatives-of-Gaussian wavelet-derived data. Discriminant analysis indicated that traditional features do not detect early proliferative retinopathy. The best single feature for discrimination was the wavelet curvature with an area under the curve (AUC) of 0.76. Linear discriminant analysis with a selection of six features achieved an AUC of 0.90 (0.73-0.97, 95% confidence interval). The wavelet method was able to segment retinal blood vessels and classify the images according to the presence or absence of proliferative retinopathy.

Feature selection environment for genomic applications

BackgroundFeature selection is a pattern recognition approach to choose important variables according to some criteria in order to distinguish or explain certain phenomena (i.e., for dimensionality reduction). There are many genomic and proteomic applications that rely on feature selection to answer questions such as selecting signature genes which are informative about some biological state, e.g., normal tissues and several types of cancer; or inferring a prediction network among elements such as genes, proteins and external stimuli. In these applications, a recurrent problem is the lack of samples to perform an adequate estimate of the joint probabilities between element states. A myriad of feature selection algorithms and criterion functions have been proposed, although it is difficult to point the best solution for each application.ResultsThe intent of this work is to provide an open-source multiplataform graphical environment for bioinformatics problems, which supports many feature selection algorithms, criterion functions and graphic visualization tools such as scatterplots, parallel coordinates and graphs. A feature selection approach for growing genetic networks from seed genes (targets or predictors) is also implemented in the system.ConclusionThe proposed feature selection environment allows data analysis using several algorithms, criterion functions and graphic visualization tools. Our experiments have shown the software effectiveness in two distinct types of biological problems. Besides, the environment can be used in different pattern recognition applications, although the main concern regards bioinformatics tasks.

Application and assessment of multiscale bending energy for morphometric characterization of neural cells

The estimation of the curvature of experimentally obtained curves is an important issue in many applications of image analysis including biophysics, biology, particle physics, and high energy physics. However, the accurate calculation of the curvature of digital contours has proven to be a difficult endeavor, mainly because of the noise and distortions that are always present in sampled signals. Errors ranging from 1% to 1000% have been reported with respect to the application of standard techniques in the estimation of the curvature of circular contours [M. Worring and A. W. M. Smeulders, CVGIP: Im. Understanding, 58, 366 (1993)]. This article explains how diagrams of multiscale bending energy can be easily obtained from curvegrams and used as a robust general feature for morphometric characterization of neural cells. The bending energy is an interesting global feature for shape characterization that expresses the amount of energy needed to transform the specific shape under analysis into its lowest energy state (i.e., a circle). The curvegram, which can be accurately obtained by using digital signal processing techniques (more specifically through the Fourier transform and its inverse, as described in this work), provides multiscale representation of the curvature of digital contours. The estimation of the bending energy from the curvegram is introduced and exemplified with respect to a series of neural cells. The masked high curvature effect is reported and its implications to shape analysis are discussed. It is also discussed and illustrated that, by normalizing the multiscale bending energy with respect to a standard circle of unitary perimeter, this feature becomes an effective means for expressing shape complexity in a way that is invariant to rotation, translation, and scaling, and that is robust to noise and other artifacts implied by image acquisition

Constructing Probabilistic Genetic Networks of Plasmodium falciparum from Dynamical Expression Signals of the Intraerythrocytic Development Cycle

The completion of the genome sequence of Plasmodium falciparum revealed that close to 60% of the annotated genome corresponds to hypothetical proteins and that many genes, whose metabolic pathways or biological products are known, have not been predicted from sequence similarity searches. Recently, using global gene expression of the asexual blood stages of P. falciparum at 1 h resolution scale and Discrete Fourier Transform based techniques, it has been demonstrated that many genes are regulated in a single periodic manner during the asexual blood stages. Moreover, by ordering the genes according to the phase of expression, a new list of targets for vaccine and drug development was generated. In the present paper, genes are annotated under a different perspective: a list of functional properties is attributed to networks of genes representing subsystems of the P. falciparum regulatory expression system. The model developed to represent genetic networks, called Probabilistic Genetic Network (PGN), is a Markov chain with some additional properties. This model mimics the properties of a gene as a non-linear stochastic gate and the systems are built by coupling of these gates. Moreover, a tool that integrates mining of dynamical expression signals by PGN design techniques, different databases and biological knowledge, was developed. The applicability of this tool for discovering gene networks of the malaria expression regulation system has been validated using the glycolytic pathway as a “gold-standard”, as well as by creating an apicoplast PGN network. Presently, we are tentatively improving the network design technique before trying to validate results from the apicoplast PGN network through reverse genetics approaches.

Interactive image segmentation by matching attributed relational graphs

A model-based graph matching approach is proposed for interactive image segmentation. It starts from an over-segmentation of the input image, exploiting color and spatial information among regions to propagate the labels from the regions marked by the user-provided seeds to the entire image. The region merging procedure is performed by matching two graphs: the input graph, representing the entire image; and the model graph, representing only the marked regions. The optimization is based on discrete search using deformed graphs to efficiently evaluate the spatial information. Note that by using a model-based approach, different interactive segmentation problems can be tackled: binary and multi-label segmentation of single images as well as of multiple similar images. Successful results for all these cases are presented, in addition to a comparison between our binary segmentation results and those obtained with state-of-the-art approaches. An implementation is available at http://structuralsegm.sourceforge.net/.

Graph-based Object Tracking Using Structural Pattern Recognition

Multidimensional projections map data points, defined in a high-dimensional data space, into a 1D, 2D or 3D representation space. Such a mapping may be typically achieved with dimensional reduction, clustering, or force directed point placement. Projections can be displayed and navigated by data analysts by means of visual representations, which may vary from points on a plane to graphs, surfaces or volumes. Typically, projections strive to preserve distance relationships amongst data points, as defined in the original space. Information loss is inevitable and the projection approach defines the extent to which the distance preserving goal is attained. We introduce PEx-the projection explorer - a visualization tool for mapping and exploration of high-dimensional data via projections. A set of examples - on both structured (table) and unstructured (text) data - illustrate how projection based visualizations, coupled with appropriate exploration tools, offer a flexible set-up for multidimensional data exploration. The projections in PEx handle relatively large data sets at a computational cost adequate to user interaction.This paper proposes a model-based methodology for recognizing and tracking objects in digital image sequences. Objects are represented by attributed relational graphs (or ARGs), which carry both local and relational information about them. The recognition is performed by inexact graph matching, which consists in finding an approximate homomorphism between ARGs derived from an input video and a model image. Searching for a suitable homomorphism is achieved through a tree-search optimization algorithm and the minimization of a pre-defined cost function. Motion smoothness between successive frames is exploited to achieve the recognition over the whole sequence, with improved spatio-temporal coherence.